Research Papers

J Biomech Eng. 2012;134(2):021001-021001-10. doi:10.1115/1.4005764.

Partial meniscectomy is believed to change the biomechanics of the knee joint through alterations in the contact of articular cartilages and menisci. Although fluid pressure plays an important role in the load support mechanism of the knee, the fluid pressurization in the cartilages and menisci has been ignored in the finite element studies of the mechanics of meniscectomy. In the present study, a 3D fibril-reinforced poromechanical model of the knee joint was used to explore the fluid flow dependent changes in articular cartilage following partial medial and lateral meniscectomies. Six partial longitudinal meniscectomies were considered under relaxation, simple creep, and combined creep loading conditions. In comparison to the intact knee, partial meniscectomy not only caused a substantial increase in the maximum fluid pressure but also shifted the location of this pressure in the femoral cartilage. Furthermore, these changes were positively correlated to the size of meniscal resection. While in the intact joint, the location of the maximum fluid pressure was dependent on the loading conditions, in the meniscectomized joint the location was predominantly determined by the site of meniscal resection. The partial meniscectomy also reduced the rate of the pressure dissipation, resulting in even larger difference between creep and relaxation times as compared to the case of the intact knee. The knee joint became stiffer after meniscectomy because of higher fluid pressure at knee compression followed by slower pressure dissipation. The present study indicated the role of fluid pressurization in the altered mechanics of meniscectomized knees.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2012;134(2):021002-021002-9. doi:10.1115/1.4005762.

The aqueous humor (AH) flow in the anterior chamber (AC) due to saccadic movements is investigated in this research. The continuity, Navier-Stokes and energy equations in 3D and unsteady forms are solved numerically and the saccadic motion was modeled by the dynamic mesh technique. Firstly, the numerical model was validated for the saccadic movement of a spherical cavity with analytic solutions and experimental data where excellent agreement was observed. Then, two types of periodic and realistic saccadic motions of the AC are simulated, whereby the flow field is computed for various saccade amplitudes and the results are reported for different times. The results show that the acting shear stress on the corneal endothelial cells from AH due to saccadic movements is much higher than that due to normal AH flow by buoyancy induced due to temperature gradient. This shear stress is higher on the central region of the cornea. The results also depict that eye saccade imposes a 3D complicated flow field in the AC consist of various vortex structures. Finally, the enchantment of heat transfer in the AC by AH mixing as a result of saccadic motion is investigated.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2012;134(2):021003-021003-7. doi:10.1115/1.4005850.

As endovascular treatment of abdominal aortic aneurysms (AAAs) gains popularity, it is becoming possible to treat certain challenging aneurysmal anatomies with endografts relying on suprarenal fixation. In such anatomies, the bare struts of the device may be placed across the renal artery ostia, causing partial obstruction to renal artery blood flow. Computational fluid dynamics (CFD) was used to simulate blood flow from the aorta to the renal arteries, utilizing patient-specific boundary conditions, in three patient models and calculate the degree of shear-based blood damage (hemolysis). We used contrast-enhanced computed tomography angiography (CTA) data from three AAA patients who were treated with a novel endograft to build patient-specific models. For each of the three patients, we constructed a baseline model and endoframe model. The baseline model was a direct representation of the patient’s 30-day post-operative CTA data. This model was then altered to create the endoframe model, which included a ring of metallic struts across the renal artery ostia. CFD was used to simulate blood flow, utilizing patient-specific boundary conditions. Pressures, flows, shear stresses, and the normalized index of hemolysis (NIH) were quantified for all patients. The overall differences between the baseline and endoframe models for all three patients were minimal, as measured though pressure, volumetric flow, velocity, and shear stress. The average NIH across the three baseline and endoframe models was 0.002 and 0.004, respectively. Results of CFD modeling show that the overall disturbance to flow caused by the presence of the endoframe struts is minimal. The magnitude of the NIH in all models was well below the accepted design and safety threshold for implantable medical devices that interact with blood flow.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2012;134(2):021004-021004-9. doi:10.1115/1.4005852.

The heterogeneous composition and mechanical properties of the supraspinatus tendon offer an opportunity for studying the structure-function relationships of fibrous musculoskeletal connective tissues. Previous uniaxial testing has demonstrated a correlation between the collagen fiber angle distribution and tendon mechanics in response to tensile loading both parallel and transverse to the tendon longitudinal axis. However, the planar mechanics of the supraspinatus tendon may be more appropriately characterized through biaxial tensile testing, which avoids the limitation of nonphysiologic traction-free boundary conditions present during uniaxial testing. Combined with a structural constitutive model, biaxial testing can help identify the specific structural mechanisms underlying the tendon’s two-dimensional mechanical behavior. Therefore, the objective of this study was to evaluate the contribution of collagen fiber organization to the planar tensile mechanics of the human supraspinatus tendon by fitting biaxial tensile data with a structural constitutive model that incorporates a sample-specific angular distribution of nonlinear fibers. Regional samples were tested under several biaxial boundary conditions while simultaneously measuring the collagen fiber orientations via polarized light imaging. The histograms of fiber angles were fit with a von Mises probability distribution and input into a hyperelastic constitutive model incorporating the contributions of the uncrimped fibers. Samples with a wide fiber angle distribution produced greater transverse stresses than more highly aligned samples. The structural model fit the longitudinal stresses well (median R2 ≥ 0.96) and was validated by successfully predicting the stress response to a mechanical protocol not used for parameter estimation. The transverse stresses were fit less well with greater errors observed for less aligned samples. Sensitivity analyses and relatively affine fiber kinematics suggest that these errors are not due to inaccuracies in measuring the collagen fiber organization. More likely, additional strain energy terms representing fiber-fiber interactions are necessary to provide a closer approximation of the transverse stresses. Nevertheless, this approach demonstrated that the longitudinal tensile mechanics of the supraspinatus tendon are primarily dependent on the moduli, crimp, and angular distribution of its collagen fibers. These results add to the existing knowledge of structure-function relationships in fibrous musculoskeletal tissue, which is valuable for understanding the etiology of degenerative disease, developing effective tissue engineering design strategies, and predicting outcomes of tissue repair.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2012;134(2):021005-021005-10. doi:10.1115/1.4005853.

Modeling of the cerebrospinal fluid (CSF) system in the spine is strongly motivated by the need to understand the origins of pathological conditions such as the emergence and growth of fluid-filled cysts in the spinal cord. In this study, a one-dimensional (1D) approximation for the flow in elastic conduits was used to formulate a model of the spinal CSF compartment. The modeling was based around a coaxial geometry in which the inner elastic cylinder represented the spinal cord, middle elastic tube represented the dura, and the outermost tube represented the vertebral column. The fluid-filled annuli between the cord and dura, and the dura and vertebral column, represented the subarachnoid and epidural spaces, respectively. The system of governing equations was constructed by applying a 1D form of mass and momentum conservation to all segments of the model. The developed 1D model was used to simulate CSF pulse excited by pressure disturbances in the subarachnoid and epidural spaces. The results were compared to those obtained from an equivalent two-dimensional finite element (FE) model which was implemented using a commercial software package. The analysis of linearized governing equations revealed the existence of three types of waves, of which the two slower waves can be clearly related to the wave modes identified in previous similar studies. The third, much faster, wave emanates directly from the vertebral column and has little effect on the deformation of the spinal cord. The results obtained from the 1D model and its FE counterpart were found to be in good general agreement even when sharp spatial gradients of the spinal cord stiffness were included; both models predicted large radial displacements of the cord at the location of an initial cyst. This study suggests that 1D modeling, which is computationally inexpensive and amenable to coupling with the models of the cranial CSF system, should be a useful approach for the analysis of some aspects of the CSF dynamics in the spine. The simulation of the CSF pulse excited by a pressure disturbance in the epidural space, points to the possibility that regions of the spinal cord with abnormally low stiffness may be prone to experiencing large strains due to coughing and sneezing.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2012;134(2):021006-021006-5. doi:10.1115/1.4005934.

The naturally occurring structure of articular cartilage has proven to be an effective means for the facilitation of motion and load support in equine and other animal joints. For this reason, cartilage has been extensively studied for many years. Although the roughness of cartilage has been determined from atomic force microscopy (AFM) and other methods in multiple studies, a comparison of roughness to joint function has not be completed. It is hypothesized that various joint types with different motions and regimes of lubrication have altered demands on the articular surface that may affect cartilage surface properties. Micro- and nanoscale stylus profilometry was performed on the carpal cartilage harvested from 16 equine forelimbs. Eighty cartilage surface samples taken from three different functioning joint types (radiocarpal, midcarpal, and carpometacarpal) were measured by a Veeco Dektak 150 Stylus Surface Profilometer. The average surface roughness measurements were statistically different for each joint. This indicates that the structure of cartilage is adapted to, or worn by, its operating environment. Knowledge of cartilage micro- and nanoscale roughness will assist the future development and design of treatments for intra- articular substances or surfaces to preserve joint integrity and reduce limitations or loss of joint performance.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2012;134(2):021007-021007-6. doi:10.1115/1.4005981.

The characterization of the biomechanical properties of newly formed bone tissue around implants is important to understand the osseointegration process. The objective of this study is to investigate the evolution of the hardness and indentation modulus of newly formed bone tissue as a function of healing time. To do so, a nanoindentation device is employed following a multimodality approach using histological analysis. Coin-shaped implants were placed in vivo at a distance of 200 μm from the cortical bone surface, leading to an initially empty cavity of 200 μm * 4.4 mm. Three New Zealand White rabbits were sacrificed after 4, 7, and 13 weeks of healing time. The bone samples were embedded and analyzed using histological analyses, allowing to distinguish mature and newly formed bone tissue. The bone mechanical properties were then measured in mature and newly formed bone tissue. The results are within the range of hardness and apparent Young’s modulus values reported in previous literature. One-way ANOVA test revealed a significant effect of healing time on the indentation modulus (p < 0.001, F = 111.24) and hardness (p < 0.02, F = 3.47) of bone tissue. A Tukey-Kramer analysis revealed that the biomechanical properties of newly formed bone tissue (4 weeks) were significantly different from those of mature bone tissue. The comparison with the results obtained in Mathieu (2011, “Micro-Brillouin Scattering Measurements in Mature and Newly Formed Bone Tissue Surrounding an Implant,” J. Biomech. Eng., 133 , 021006). shows that bone mass density increases by approximately 13.5% between newly formed bone (7 weeks) and mature bone tissue.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2012;134(2):021008-021008-14. doi:10.1115/1.4006026.

Atrial fibrillation (AF) is a cardiac arrhythmia that highly increases the risk of stroke and is associated with significant but still unexplored changes in the mechanical behavior of the tissue. Planar biaxial tests were performed on tissue specimens from pigs at the healthy stage and after ventricular tachypacing (VTP), a procedure applied to reproduce the relevant features of AF. The local arrangement of the fiber bundles in the tissue was investigated on specimens from rabbit atria by means of circularly polarized light. Based on this, mechanical data were fitted to two anisotropic constitutive relationships, including a four-parameter Fung-type model and a microstructurally-motivated model. Accounting for the fiber-induced anisotropy brought average R2  = 0.807 for the microstructurally-motivated model and average R2  = 0.949 for the Fung model. Validation of the fitted constitutive relationships was performed by means of FEM simulations coupled to FORTRAN routines. The performances of the two material models in predicting the second Piola-Kirchhoff stress were comparable, with average errors <3.1%. However, the Fung model outperformed the other in the prediction of the Green-Lagrange strain, with 9.2% maximum average error. To increase model generality, a proper averaging procedure accounting for nonlinearities was used to obtain average material parameters. In general, a stiffer behavior after VTP was noted.

Commentary by Dr. Valentin Fuster

Technical Briefs

J Biomech Eng. 2012;134(2):024501-024501-7. doi:10.1115/1.4005696.

In the presence of a tumor defect, completed humeral shaft fractures continue to be a major surgical challenge since there is no “gold standard” treatment. This is due, in part, to the fact that only one prior biomechanical study exists on the matter, but which only compared 2 repair methods. The current authors measured the humeral torsional performance of 5 fixation constructs for completed pathological fractures. In 40 artificial humeri, a 2-cm hemi-cylindrical cortical defect with a transverse fracture was created in the lateral cortex. Specimens were divided into 5 different constructs and tested in torsion. Construct A was a broad 10-hole 4.5-mm dynamic compression plate (DCP). Construct B was the same as A except that the screw holes and the tumor defect were filled with bone cement and the screws were inserted into soft cement. Construct C was the same as A except that the canal and tumor defect were filled with bone cement and the screws were inserted into dry cement. Construct D was a locked intramedullary nail inserted in the antegrade direction. Construct E was the same as D except that bone cement filled the defect. For torsional stiffness, construct C (4.45 ± 0.20 Nm/deg) was not different than B or E (p > 0.16), but was higher than A and D (p < 0.001). For failure torque, construct C achieved a higher failure torque (69.65 ± 5.35 Nm) than other groups (p < 0.001). For the failure angle, there were no differences between plating constructs A to C (p ≥ 0.11), except for B versus C (p < 0.05), or between nailing groups D versus E (p = 0.97), however, all plating groups had smaller failure angles than both nailing groups (p < 0.05). For failure energy, construct C (17.97 ± 3.59 J) had a higher value than other groups (p < 0.005), except for A (p = 0.057). Torsional failure always occurred in the bone in the classic “spiral” pattern. Construct C provided the highest torsional stability for a completed pathological humeral shaft fracture.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2012;134(2):024502-024502-7. doi:10.1115/1.4005693.

Accurate material properties of developing embryonic tissues are a crucial factor in studies of the mechanics of morphogenesis. In the present work, we characterize the viscoelastic material properties of the looping heart tube in the chick embryo through nonlinear finite element modeling and microindentation experiments. Both hysteresis and ramp-hold experiments were performed on the intact heart and isolated cardiac jelly (extracellular matrix). An inverse computational method was used to determine the constitutive relations for the myocardium and cardiac jelly. With both layers assumed to be quasilinear viscoelastic, material coefficients for an Ogden type strain-energy density function combined with Prony series of two terms or less were determined by fitting numerical results from a simplified model of a heart segment to experimental data. The experimental and modeling techniques can be applied generally for determining viscoelastic material properties of embryonic tissues.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2012;134(2):024503-024503-9. doi:10.1115/1.4005761.

The normal periodic turnover of bone is referred to as remodeling. In remodeling, old or damaged bone is removed during a ‘resorption’ phase and new bone is formed in its place during a ‘formation’ phase in a sequence of events known as coupling. Resorption is preceded by an ‘activation’ phase in which the signal to remodel is initiated and transmitted. Remodeling is known to involve the interaction of external stimuli, bone cells, calcium and phosphate ions, and several proteins, hormones, molecules, and factors. In this study, a semi-empirical cell dynamics model for bone remodeling under external stimulus that accounts for the interaction between bone mass, bone fluid calcium, bone calcium, and all three major bone cell types, is presented. The model is formulated to mimic biological coupling by solving separately and sequentially systems of ODEs for the activation, resorption, and formation phases of bone remodeling. The charateristic time for resorption (20 days) and the amount of resorption (∼0.5%) are fixed for all simulations, but the formation time at turnover is an output of the model. The model was used to investigate the effects of different types of strain stimuli on bone turnover under bone fluid calcium balance and imbalance conditions. For bone fluid calcium balance, the model predicts complete turnover after 130 days of formation under constant 1000 microstrain stimulus; after 47 days of formation under constant 2000 microstrain stimulus; after 173 days of formation under strain-free conditions, and after 80 days of formation under monotonic increasing strain stimulus from 1000 to 2000 microstrain. For bone fluid calcium imbalance, the model predicts that complete turnover occurs after 261 days of formation under constant 1000 microstrain stimulus and that turnover never occurs under strain-free conditions. These predictions were not impacted by mean dynamic input strain stimuli of 1000 and 2000 microstrain at 1 Hz and 1000 microstrain amplitude. The formation phase of remodeling lasts longer than the resorption phase, increased strain stimulus accelerates bone turnover, while absence of strain significantly delays or prevents it, and formation time for turnover under monotonic increasing strain conditions is intermediate to those for constant strain stimuli at the minimum and maximum monotonic strain levels. These results are consistent with the biology, and with Frost’s mechanostat theory.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2012;134(2):024504-024504-4. doi:10.1115/1.4006116.

Strain is an essential metric in tissue mechanics. Strains and strain distributions during functional loads can help identify damaged and pathologic regions as well as quantify functional compromise. Noninvasive strain measurement in vivo is difficult to perform. The goal of this in vitro study is to determine the efficacy of digital image correlation (DIC) methods to measure strain in B-mode ultrasound images. The Achilles tendons of eight male Wistar rats were removed and mechanically cycled between 0 and 1% strain. Three cine video images were captured for each specimen: (1) optical video for manual tracking of optical markers; (2) optical video for DIC tracking of optical surface markers; and (3) ultrasound video for DIC tracking of image texture within the tissue. All three imaging modalities were similarly able to measure tendon strain during cyclic testing. Manual/ImageJ-based strain values linearly correlated with DIC (optical marker)-based strain values for all eight tendons with a slope of 0.970. DIC (optical marker)-based strain values linearly correlated with DIC (ultrasound texture)-based strain values for all eight tendons with a slope of 1.003. Strain measurement using DIC was as accurate as manual image tracking methods, and DIC tracking was equally accurate when tracking ultrasound texture as when tracking optical markers. This study supports the use of DIC to calculate strains directly from the texture present in standard B-mode ultrasound images and supports the use of DIC for in vivo strain measurement using ultrasound images without additional markers, either artificially placed (for optical tracking) or anatomically in view (i.e., bony landmarks and/or muscle-tendon junctions).

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2012;134(2):024505-024505-6. doi:10.1115/1.4006199.

Polyvinyl alcohol (PVA) cryogel covered stents may reduce complications from thrombosis and restenosis by decreasing tissue prolapse. Finite element analysis was employed to evaluate the effects of PVA cryogel layers of varying thickness on tissue prolapse and artery wall stress for two common stent geometries and two vessel diameters. Additionally, several PVA cryogel covered stents were fabricated and imaged with an environmental scanning electron microscope. Finite element results showed that covered stents reduced tissue prolapse up to 13% and artery wall stress up to 29% with the size of the reduction depending on the stent geometry, vessel diameter, and PVA cryogel layer thickness. Environmental scanning electron microscope images of expanded covered stents showed the PVA cryogel to completely cover the area between struts without gaps or tears. Overall, this work provides both computational and experimental evidence for the use of PVA cryogels in covered stents.

Commentary by Dr. Valentin Fuster

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